C₁₆×D₈ #12037

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×C₄×#3003 (order 2048) · Inn(G) = D₄ · Out(G) = C₂³×C₄×D₄
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

C₁₆×D₈

129 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);(17,18,19,20,21,22,23,24);(18,24)(19,23)(20,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5025);